What is the inverse of #f(x) = 3^x# ?

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What is the inverse of #f(x) = 3^x# ?

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Answer 1 · 2015-11-02T01:39:24

I found: #g(x)=log_3(x)#

Explanation:

You can take the log in base 3 of both sides to isolate #x# as:
#log_3(f(x))=log_3(3^x)# where we can cancel #log_3# with#3#;
So:
#log_3(f(x))=x#
This can be written as the inverse function changing #x# with #g(x)# and #f(x)# with #x# as:
#g(x)=log_3(x)#

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What is the inverse of #f(x) = 3^x# ?

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